tel

17 ms·

61.
by tel 2y ago
You could think of it as a proof saying which polynomials are solvable by which algorithms. Solvable by radicals is one class of simpler algorithm and it so happens we have a cute proof as to when it will work or fail.
62.
by tel 2y ago
In short, tensors generalize matrices. While we can probably guess accurately what "4x4 matrix" means, "4x4 tensor" is missing some information to really nail down what it means. Interestingly, that extra information hel
63.
by tel 2y ago
Not really to push back as I do agree that this is a bit trickier to get an intuition for than the OP suggests, but the most trivial concrete example of a (1, 1) tensor would just be the evaluation function (v, f) |-> f(v), which, given
64.
by tel 2y ago
It also suggests the argument generalizes to symbols as non-compact sets.
65.
by tel 2y ago
I think that’s right, though it’s non-obvious that more probable systems are disordered. At least as non-obvious as Pascal’s triangle is. Which is to say, worth saying from a first principles POV, but not all that startling.
66.
by tel 2y ago
You can sort of do this over a suitably large (or infinite) family of models all mixed, but from an epistemological POV that’s pretty unsatisfying. From a practical POV it’s pretty useful and common (if you allow it to describe non- and sem
67.
by tel 2y ago
I don't think that implementation is particularly good, although this is a big trick with Sans-IO: is the event loop responsible for buffering the input bytes? Or are the state machines? In effect, you have to be thoughtful (and explic
68.
by tel 2y ago
I agree totally, it wasn't my intention to say that there aren't protocols which require non-trivial state machines to implement their behavior. To be more clear, I'm contesting that the only thing being discussed in the arti
69.
by tel 2y ago
I don't think that's quite true. The lift here is that the state machine does not do any IO on its own. It always delegates that work to the event loop that's hosting it, which allows it to be interpreted in different context
70.
by tel 2y ago
For sure, string diagrams are meant as a tool for someone experienced with category theoretic proofs. It's possible that they could be used in introductory material too--a la that quantum book that's very diagrammatic--but this pa
71.
by tel 2y ago
String diagrams are also pretty confusing if you're not already very comfortable with category theory. They exist to make complex equality proofs a little easier, but the underlying proofs themselves are not easy to follow.
72.
by tel 2y ago
I don't. I've never actually seen interval theory developed like I did above. It's just me porting parts of probability theory over to solve the same problems as they appear in talking about intervals.
73.
by tel 2y ago
To say it explicitly, string diagrams are nice exactly because they convert category theoretic equivalences into topological equivalences that are easy to read visually.
74.
by tel 2y ago
It's been a while since I read these, but I believe it's because h is below alpha. They're exploiting the "sliding equality" referenced at the bottom of page 7.
75.
by tel 2y ago
I think a more complete way to say it would be that probability theory is a refinement of interval theory. Per that last remark, I suspect that if you add any probability measure to intervals such that it has positive weight along the lengt
76.
by tel 2y ago
There's some abuse of poor notation going on in the article. I don't think the author is intending to be confusing through this imprecision, but instead is just faithfully representing the common way people discuss this kind of st
77.
by tel 2y ago
It's hard for me to understand the goal of this comment. Nothing in it is incorrect. It's also not really a meaningful critique or response to the article. The article did not attempt to describe "uncertainty analysis for sci
78.
by tel 2y ago
Tom7 is a somewhat well-known mad computer scientist who specializes in technically ambitious projects of limited utility. In this latest escapade, he takes inspiration from Knuth's line-packing algorithm used in typesetting beautiful
79.
by tel 2y ago
They target the residual stream. Also they may have a definition of “feature” that’s more general than what you’re using. Consider reading their superposition work.
80.
by tel 2y ago
This is exceptionally cool. Not only is it very interesting to see how this can be used to better understand and shape LLM behavior, I can’t help but also think it’s an interesting roadmap to human anthropology. If we see LLMs as substantia
81.
by tel 2y ago
Can we change the title to something like "Show HN: 'TL;DR AI', community-written abstracts for research papers"? The name of the project, "TL;DR AI", seems to be causing grammatical confusion. It's easy t
82.
by tel 2y ago
I think there's a bit of a straw man here pointing at the series definitions as being applied as the "intuitive" sense for sin and cos. Instead, I find that the intuition that's sought is more to start by seeing exp(it)
83.
by tel 3y ago
To make matters stronger there are significant tax benefits (the public subsidizing private home ownership) and the US’s 30y fixed rate loan is startlingly good, especially since you have a refinancing option. The risk of these loans is aga
84.
by tel 3y ago
I think part of what I suspect is going on here too is more computation and finiteness. It seems correct that LLM architectures cannot perform too much computation (unless you unroll it in the context). On the other hand you can look at sta
85.
by tel 3y ago
I thought the examples I was thinking of were in the original GPT-4 Technical Report, but all I found on re-reading were examples of it explaining "what's funny about" a given image. Which is still a decent example of this, I
86.
by tel 3y ago
Okay I think I buy that. I don’t know if I agree, but trying to argue for a position against it has been sufficiently illuminating that I just need to chew on it more. There’s no doubt in my mind that experimental learning is more efficient
87.
by tel 3y ago
So we craft experiments. If someone else crafted an experiment, and you were informed of it and then shown the results, if this was done repeatedly enough, would you be incapable of forming any sort of semantic meaning?
88.
by tel 3y ago
Okay, I think I follow and agree legalistically with your argument. But I also think it basically only exists philosophically. In practice, we make these determinations all the time. I don't see any reason why a sufficiently sophistica
89.
by tel 3y ago
Do you have a reference on “random linear projections as memorization”? I know random projections quite well but haven’t seen that connection.
90.
by tel 3y ago
That suggests that no statistical method could ever recover hidden representations though. And that’s patently untrue. Taken to its greatest extreme you shouldn’t even be able to guess between two mixed distributions even when they have wil

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